Il tappeto polveroso è davanti al divano in soggiorno.

In Italian, singular countable nouns almost always take an article.

• Il tappeto (“the carpet”) indicates a specific carpet known in context (e.g. the one you’ve been looking at).
• Un tappeto would mean “a (some) carpet,” introducing it for the first time or speaking of any carpet in general.
• Omitting the article entirely (just saying tappeto) is ungrammatical when you mean “the carpet.”

Italian descriptive adjectives normally follow the noun: tappeto polveroso.

• Putting the adjective before (polveroso tappeto) is not wrong, but it sounds poetic, old-fashioned or emphatic.
• Most learners will hear and use the post-noun position for neutral descriptions.

The suffix -oso means “full of” or “characterized by.”

• Polvere = “dust”
• Polveroso = “dusty; full of dust”
  This suffix is found in many adjectives: grembiule fangoso (“muddy apron”), occhi luminosi (“bright eyes”), etc.

Davanti is an adverb meaning “in front.” When you link it to a noun, you use the preposition a: davanti a.

• A + il divano contracts to al divano, giving davanti al divano (“in front of the sofa”).
• If the noun were feminine singular (la porta), you’d get davanti alla porta.

Yes, di fronte a also means “in front of.”

• Di fronte al divano is slightly more formal or stresses a straight-on, face-to-face position.
• Davanti al divano is very common in everyday speech and perfectly interchangeable in most contexts.

With rooms and spaces inside buildings, Italians often omit the article after in:

• in soggiorno, in cucina, in salotto, in ufficio.
  That’s idiomatic and sounds more natural.
  You can still say nel soggiorno (“in the living room”) if you want to emphasize the room itself, but the articleless form is preferred in casual speech.

È is the simple linking verb “is,” okay for stating locations:

• Il tappeto polveroso è davanti al divano = “The dusty carpet is in front of the sofa.”
  If you want to emphasize “location,” you can use trovarsi:
• Il tappeto polveroso si trova davanti al divano
  This version is more formal or descriptive but means essentially the same thing.